david wong

Hey ! I'm David, a security consultant at Cryptography Services, the crypto team of NCC Group . This is my blog about cryptography and security and other related topics that I find interesting.

Same RSA modulus and correlated public exponents April 2015

Plaid, The biggest CTF Team, was organizing a Capture The Flag contest last week. There were two crypto challenges that I found interesting, here is the write-up of the second one:

You are given a file with a bunch of triplets:

{N : e : c}

and the hint was that they were all encrypting the same message using RSA. You could also easily see that N was the same modulus everytime.

The trick here is to find two public exponent \( e \) which are coprime: \( gcd(e_1, e_2) = 1 \)

This way, with Bézout's identity you can find \( u \) and \( v \) such that: \(u \cdot e_1 + v \cdot e_2 = 1 \)

So, here's a little sage script to find the right public exponents in the triplets:

for index, triplet in enumerate(truc[:-1]):
    for index2, triplet2 in enumerate(truc[index+1:]):
        if gcd(triplet[1], triplet2[1]) == 1:
            a = index
            b = index2
            c = xgcd(triplet[1], triplet2[1])

Now that have found our \( e_1 \) and \( e_2 \) we can do this:

\[ c_1^{u} * c_2^{v} \pmod{N} \]

And hidden underneath this calculus something interesting should happen:

\[ (m^{e_1})^u * (m^{e_2})^u \pmod{N} \]

\[ = m^{u \cdot e_1 + v \cdot e_2} \pmod{N} \]

\[ = m \pmod{N} \]

And since \( m < N \) we have our solution :)

Here's the code in Sage:

m = Mod(power_mod(e_1, u, N) * power_mod(e_2, v, N), N)

And after the crypto part, we still have to deal with the presentation part:

hex_string = "%x" % m
import binascii

Tadaaa!! And thanks @spdevlin for pointing me in the right direction :)

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Plaid CTF April 2015

The Plaid Parliament of Pwning, a security team at Carnegie Mellon University is organizing a CTF right now until tomorrow: http://play.plaidctf.com/

There are two crypto challenges at the moment, and maybe more if someone unlocks one. Have fun!

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What are x509 certificates? RFC? ASN.1? DER? April 2015


So, RFC means Request For Comments and they are a bunch of text files that describe different protocols. If you want to understand how SSL, TLS (the new SSL) and x509 certificates (the certificates used for SSL and TLS) all work, for example you want to code your own OpenSSL, then you will have to read the corresponding RFC for TLS: rfc5280 for x509 certificates and rfc5246 for the last version of TLS (1.2).

rfc ex


x509 is the name for certificates which are defined for:

informal internet electronic mail, IPsec, and WWW applications

There used to be a version 1, and then a version 2. But now we use the version 3. Reading the corresponding RFC you will be able to read such structures:

Certificate  ::=  SEQUENCE  {
    tbsCertificate       TBSCertificate,
    signatureAlgorithm   AlgorithmIdentifier,
    signatureValue       BIT STRING  }

those are ASN.1 structures. This is actually what a certificate should look like, it's a SEQUENCE of objects.

  • The first object contains everything of interest that will be signed, that's why we call it a To Be Signed Certificate
  • The second object contains the type of signature the CA used to sign this certificate (ex: sha256)
  • The last object is not an object, its just some bits that correspond to the signature of the TBSCertificate after it has been encoded with DER


It looks small, but each object has some depth to it.

The TBSCertificate is the biggest one, containing a bunch of information about the client, the CA, the publickey of the client, etc...

TBSCertificate  ::=  SEQUENCE  {
    version         [0]  EXPLICIT Version DEFAULT v1,
    serialNumber         CertificateSerialNumber,
    signature            AlgorithmIdentifier,
    issuer               Name,
    validity             Validity,
    subject              Name,
    subjectPublicKeyInfo SubjectPublicKeyInfo,
    issuerUniqueID  [1]  IMPLICIT UniqueIdentifier OPTIONAL,
                         -- If present, version MUST be v2 or v3
                          subjectUniqueID [2]  IMPLICIT UniqueIdentifier OPTIONAL,
                      -- If present, version MUST be v2 or v3
     extensions      [3]  EXPLICIT Extensions OPTIONAL
                      -- If present, version MUST be v3


A certificate is of course not sent like this. We use DER to encode this in a binary format.

Every fieldname is ignored, meaning that if we don't know how the certificate was formed, it will be impossible for us to understand what each value means.

Every value is encoded as a TLV triplet: [TAG, LENGTH, VALUE]

For example you can check the GITHUB certificate here

github cert

On the right is the hexdump of the DER encoded certificate, on the left is its translation in ASN.1 format.

As you can see, without the RFC near by we don't really know what each value corresponds to. For completeness here's the same certificate parsed by openssl x509 command tool:

x509 openssl parsed

How to read the DER encoded certificate

So go back and check the hexdump of the GITHUB certificate, here is the beginning:

30 82 05 E0 30 82 04 C8 A0 03 02 01 02

As we saw in the RFC for x509 certificates, we start with a SEQUENCE.

Certificate  ::=  SEQUENCE  {

Microsoft made a documentation that explains pretty well how each ASN.1 TAG is encoded in DER, here's the page on SEQUENCE

30 82 05 E0

So 30 means SEQUENCE. Since we have a huge sequence (more than 127 bytes) we can't code the length on the one byte that follows:

If it is more than 127 bytes, bit 7 of the Length field is set to 1 and bits 6 through 0 specify the number of additional bytes used to identify the content length.

(in their documentation the least significant bit on the far right is bit zero)

So the following byte 82, converted in binary: 1000 0010, tells us that the length of the SEQUENCE will be written in the following 2 bytes 05 E0 (1504 bytes)

We can keep reading:

30 82 04 C8 A0 03 02 01 02

Another Sequence embedded in the first one, the TBSCertificate SEQUENCE

TBSCertificate  ::=  SEQUENCE  {
    version         [0]  EXPLICIT Version DEFAULT v1,

The first value should be the version of the certificate:

A0 03

Now this is a different kind of TAG, there are 4 classes of TAGs in ASN.1: UNIVERSAL, APPICATION, PRIVATE, and context-specific. Most of what we use are UNIVERSAL tags, they can be understood by any application that knows ASN.1. The A0 is the [0] (and the following 03 is the length). [0] is a context specific TAG and is used as an index when you have a series of object. The github certificate is a good example of this, because you can see that the next index used is [3] the extensions object:

TBSCertificate  ::=  SEQUENCE  {
    version         [0]  EXPLICIT Version DEFAULT v1,
    serialNumber         CertificateSerialNumber,
    signature            AlgorithmIdentifier,
    issuer               Name,
    validity             Validity,
    subject              Name,
    subjectPublicKeyInfo SubjectPublicKeyInfo,
    issuerUniqueID  [1]  IMPLICIT UniqueIdentifier OPTIONAL,
                         -- If present, version MUST be v2 or v3
                          subjectUniqueID [2]  IMPLICIT UniqueIdentifier OPTIONAL,
                      -- If present, version MUST be v2 or v3
     extensions      [3]  EXPLICIT Extensions OPTIONAL
                      -- If present, version MUST be v3

Since those obects are all optionals, skipping some without properly indexing them would have caused trouble parsing the certificate.

Following next is:

02 01 02

Here's how it reads:

  _______ tag:      integer
 |   ____ length: 1 byte
 |  |   _ value:  2
 |  |  |
 |  |  |
 v  v  v
02 01 02 

The rest is pretty straight forward except for IOD: Object Identifier.

Object Identifiers

They are basically strings of integers that reads from left to right like a tree.

So in our Github's cert example, we can see the first IOD is 1.2.840.113549.1.1.11 and it is supposed to represent the signature algorithm.

So go to http://www.alvestrand.no/objectid/top.html and click on 1, and then 1.2, and then 1.2.840, etc... until you get down to the latest branch of our tree and you will end up on sha256WithRSAEncryption.

Here's a more detailed explanation on IOD and here's the microsoft doc on how to encode IOD in DER.

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Cryptography Services to audit Let's Encrypt April 2015

Like the audit of OpenSSL wasn't awesome enough, today we learned that we were going to audit Let's Encrypt this summer as well. Pretty exciting agenda for an internship!


ISRG has engaged the NCC Group Crypto Services team to perform a security review of Let’s Encrypt’s certificate authority software, boulder, and the ACME protocol. NCC Group’s team was selected due to their strong reputation for cryptography expertise, which brought together Matasano Security, iSEC Partners, and Intrepidus Group.

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ASN.1 vs DER vs PEM vs x509 vs PKCS#7 vs .... April 2015

I was really confused about all those acronyms when I started digging into OpenSSL and RFCs. So here's a no bullshit quick intro to them.


Or Public-Key Crypto Standard number 7. It's just a guideline, set of rules, on how to send messages, sign messages, etc... There are a bunch of PKCS that tells you exactly how to do stuff using crypto. PKCS#7 is the one who tells you how to sign and encrypt messages using certificates. If you ever see "pkcs#7 padding", it just refers to the padding explained in pkcs#7.


In a lot of things in the world (I'm being very vague), we use certificates. For example each person can have a certificate, and each person's certificate can be signed by the government certificate. So if you want to verify that this person is really the person he pretends to be, you can check his certificate and check if the government signature on his certificate is valid.

TLS use x509 certificates to authenticate servers. If you go on https://www.facebook.com, you will first check their certificate, see who signed it, checked the signer's certificate, and on and on until you end up with a certificate you can trust. And then! And only then, you will encrypt your session.

So x509 certificates are just objects with the name of the server, the name of who signed his certificate, the signature, etc...

Example from wikipedia:

        Serial Number
        Algorithm ID
            Not Before
            Not After
        Subject Public Key Info
            Public Key Algorithm
            Subject Public Key
        Issuer Unique Identifier (optional)
        Subject Unique Identifier (optional)
        Extensions (optional)
    Certificate Signature Algorithm
    Certificate Signature


So, how should we write our certificate in a computer format? There are a billion ways of formating a document and if we don't agree on one then we will never be able to ask a computer to parse a x509 certificate.

That's what ASN.1 is for, it tells you exactly how you should write your object/certificate


ASN.1 defines the abstract syntax of information but does not restrict the way the information is encoded. Various ASN.1 encoding rules provide the transfer syntax (a concrete representation) of the data values whose abstract syntax is described in ASN.1.

Now to encode our ASN.1 object we can use a bunch of different encodings specified in ASN.1, the most common one being used in TLS is DER

DER is a TLV kind of encoding, meaning you first write the Tag (for example, "serial number"), and then the Length of the following value, and then the Value (in our example, the serial number).

DER is also more than that:

DER is intended for situations when a unique encoding is needed, such as in cryptography, and ensures that a data structure that needs to be digitally signed produces a unique serialized representation.

So there is only one way to write a DER document, you can't re-order the elements.

And a made up example for an ASN.1 object:

&operationCode INTEGER UNIQUE,




And its DER encoding:

0110 0111 0010 110...


Base64 is just a way of writing binary data in a string, so you can pass it to someone on facebook messenger for exemple

From the openssl Wiki:


And if you see any equal sign =, it's for padding.

So if the first 6 bits of your file is '01' in base 10, then you will write that as B in plaintext. See an example if you still have no idea about what I'm talking about.


A pem file is just two comments (that are very important) and the data in base64 in the middle. For example the pem file of an encrypted private key:


And yes the number of - are important

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Video: How the RSA attacks using lattices work April 2015

This is my second video, after the first explaining how DPA works. I'm still trying to figure out how to do that but I think it is already better than the first one. Here I explain how Coppersmith used LLL, an algorithm to reduce lattices basis, to attack RSA. I also explain how his attack was simplified by Howgrave-Graham, and the following Boneh and Durfee attack simplified by Herrmann and May as well.

The repo is here, you can check the survey here as well.

Also, follow me on twitter

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encryption with a one letter XOR? Really? April 2015

So there is this app that encrypts your data on your mobile, in case it ends up in the wrong hands. Sounds good. And then there is this guy who took a look at it and figured out the data was just XORed with a 128bit keys consisting of only 4s. If the data is longer than 128bits? Let's not encrypt it!

I don't know how legit it is, especially considering how easy it is to just write aes(something) but here you go

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Unix command of the day: Tee April 2015

The tee command allow you to write to a file and still display the result in output.

For exemple


display the content of the current folder in stdout (the terminal)

ls > file.txt

saves that in a file file.txt

ls | tee file.txt

saves that in a file file.txt and displays in stdout at the same time

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Truecrypt report April 2015

Some news about the Truecrypt open audit: the report is out.

The TL;DR is that based on this audit, Truecrypt appears to be a relatively well-designed piece of crypto software. The NCC audit found no evidence of deliberate backdoors, or any severe design flaws that will make the software insecure in most instances.

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I'm officialy an intern at Cryptography Services April 2015

I haven't been posting for a while, and this is because I was busy looking for a place in Chicago. I finally found it! And I just accomplished my first day at Cryptography Services, or rather at Matasano since I'm in their office, or rather at NCC Group since everything must be complicated :D

I arrived and received a bag of swags along with a brand new macbook pro! That's awesome except for the fact that I spent way too much time trying to understand how to properly use it. A few things I've discovered:

  • you can pipe to pbcopy and use pbpaste to play with the clipboard
  • open . in the console opens the current directory in Finder (on windows with cygwin I use explorer .)
  • in the terminal preference: check "use option as meta key" to have all the unix shortcuts in the terminal (alt+b, ctrl+a, etc...)
  • get homebrew to install all the things

I don't know what I'll be blogging about next, because I can't really disclose the work I'll be doing there. But so far the people have been really nice and welcoming, the projects seem to be amazingly interesting (and yeah, I will be working on OpenSSL!! (the audit is public so that I can say :D)). The city is also amazing and I've been really impressed by the food. Every place, every dish and every bite has been a delight :)

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Cryptool... March 2015

I just discovered Cryptool. I can't believed I didn't know about that earlier.

The CrypTool Portal raises awareness and interest in encryption techniques for everyone. All learning programs in the CrypTool project are open source and available for free. The CrypTool project develops the world most-widespread free e-learning programs in the area of cryptography and cryptoanalysis.

On their main page (cryptool portal) you have links to: Cryptool 1, Cryptool 2, JCryptool, Cryptool Online and Mystery Twister C3. Each project is a huge amount of information that was gathered by a group of volunteer (so yeah, for free). There are tons of tutorials and ways to play with ciphers to understand them. There is even a coppersmith and boneh-durfee explanation/implementation of the attacks I implemented these last months... This is huge. I feel like I'm just discovering the tip of the iceberg and it's all really confusing so here's a recap of what is everything, for me and for you :)

Cryptool 1


CrypTool 1 (CT1) was the first version of CrypTool. It was released in 1998 and allows to experiment with different cryptographic algorithms. CT1 runs under Windows. CT1 has two successors: CT2 and JCT.

It doesn't seem like it's useful to dig into this one since CT2 and JCT are supposed to be the updated versions. I've still installed it and it looks really old! But it's super complete and super fast so... still super useful.

Cryptool 2


CrypTool 2 (CT2) supports visual programming and execution of cascades of cryptographic procedures. CT2 also runs under Windows.

I skimmed through it seeing no resemblance to CT1. I have to spend more time with it but CT1 seemed way more educational and complete...



JCrypTool (JCT) is platform-independent and runs under Linux, Mac and Windows.

Haven't tried it yet but it looks like a multiplatform CT2

Cryptool Online

CrypTool-Online (CTO) was released in spring 2009. This tool allows to try out different algorithms in a browser / smartphone.

I'm gonna be honest here, not really nice compared to CT1 and CT2. Pretty limited.

Mystery Twister C3

You like riddles? You always loved to solve the crosswords in your newspaper? Or maybe you are just curious and want to find out about some of the ways to hide a secret (and possibily even to uncover it)? This is your place! Here at MysteryTwister C3 you can solve crypto challenges, starting from the simple Caesar cipher all the way to modern AES we have challenges for everyone.

The first riddle is just a sequence a number where you have to guess the last entry. Typical IQ test but it has been solved by 2138 people.

The 29th riddle is Hadstad broadcast attack and had only been solved by 102 people.

There are raffles every month so it might be a nice playground :) play here

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